The equitable presentation for the quantum group $U_q(g)$ associated with a symmetrizable Kac-Moody algebra $g$
Abstract
Description
We consider the quantum group $U_q(g)$ associated with a symmetrizable Kac-Moody algebra $g$. We display a presentation for $U_q(g)$ that we find attractive; we call this the equitable presentation. For $g=sl_2$ the equitable presentation has generators $X,X^{-1},Y,Z$ and relations
$X X^{-1} =1$,
$X^{-1} X=1$,
$\frac{qXY-q^{-1}YX}{q-q^{-1}}=1$,
$\frac{qYZ-q^{-1}ZY}{q-q^{-1}}=1$,
$\frac{qZX-q^{-1}XZ}{q-q^{-1}}=1$.
16 pages. Submitted to J. Algebra
16 pages. Submitted to J. Algebra